Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int a[200010],b[200010],c[200010];

int main()
{
    //freopen("input.txt","r",stdin);
    int n;scanf("%d",&n);
    for (int i=1;i<=n;i++) {scanf("%d",&a[i]);b[a[i]]=i;}
    int k=n;
    while (k>1&&b[k-1]<b[k]) k--;
    int i=0;c[0]=k;
    while (c[i]>1)
    {
        int k=c[i]-1;
        while (k>1)
        {
            if (b[c[i]]<b[k-1]&&b[k-1]<b[k]||b[k-1]<b[k]&&b[k]<b[c[i]]||b[k]<b[c[i]]&&b[c[i]]<b[k-1]) {k--;continue;}
            break;
        }
        c[++i]=k;
    }
    printf("%d\n",i);
    return 0;
}